Effects of diabaticity on fusion of heavy nuclei in the dinuclear model ...

Appendix B
The collective response function [86] can be derived by introducing a (hypothetical) external
force ˆ F fext(t) and by evaluating how the deviation <strong>of</strong> < ˆ F >ω from some properly chosen
static value reacts to this external field in linear order
δ< ˆ F>ω= − χ coll(ω) · f ext(ω). (B.1)
The collective response function can be brought to the form [86]
coll(ω) = χ χ(ω)
. (B.2)
1+kχ(ω)
Here, χ(ω) is the Fourier transform <strong>of</strong> the response function for intrinsic motion. Its time-
dependent version reads
˜
(t − s) =ϑ(t − s) χ i
¯h
tr
qs(Q0,T0) ρ
ˆ F(s) (t), ˆF
, (B.3)
where ϑ(x) is the Heavyside’s function. In the expression (B.3) the time development <strong>of</strong> the
field operators is defined by the same Hamiltonian ˆ H(xi,p i,Q) which appears in the density
ρ qs.
The coupling constant k is written in the form
−k −1 =< ∂2H(xi,pi,Q) ˆ
∂Q2 >Q0,T0= ∂2 S0) E(Q,
∂Q2 + χ(ω =0)=C(0) + χ(0) (B.4)
|Q0
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